Two-wheeled cart falls under kinematically deficient manipulator when considered from cooperating manipulator approach. Kinematically deficient manipulators are those that have fewer degrees of freedom than necessary to achieve any admissible configuration in their operational space. When multiple manipulators, some or all of which are kinematically deficient, cooperate to perform a common task, the constrained forces at the contact points cannot be solved directly due to rank deficiency of the jacobian. This paper addresses this challenge associated with the computation of constrained forces at the contact points by introducing a novel approach called "pseudo joint." Forward dynamical model utilizing pseudo joint has been driven for cooperating kinematically deficient manipulators. Dynamics of two-wheeled cart has been given to demonstrate the methodology.